Is $f (x) = e^{3 - 3 x} + \frac{x}{ln 2} x$ $f(x)=e^(3-3x)+x/ln2x$ concave or convex at $x = 1$ $x=1$ ?

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Answer 1 · 2016-05-16T11:39:07

$f (x)$ $f(x)$ is concave for $\forall x > 2.11$ $AA x>2.11$ and convex for $\forall 0 < x < 2.11$ $AA 0<x<2.11$

The zero of the second derivation
$f''(x)=9*e^(3-3x)-2/(ln(2)$ is at $x=2.11$
That's where the function changes it's bending behaviour.

Is f(x)=e^(3-3x)+x/ln2xf(x)=e3−3x+xln2xf(x)=e^(3-3x)+x/ln2x concave or convex at x=1x=1x=1?